Firstly, people proposed that the photon orbits signals a possible York-Hawking-Page phase transition in Refs. [1]}, [2]}. Then the more clearly relation between photon orbits and phase transitions of Reissner-Nordstrom-AdS black hole and rotating Kerr-AdS black hole were shown in Ref. [3]}. Namely, the photon orbit radius and the minimum impact parameter along with the temperature are both exhibiting non-monotonic behaviours for the low pressure, whose behaviours are indeed the characters of the phase transition existence. Particularly, the changes of those two quantities near the critical point could be treated as the order parameters of phase transition, and they have an universal exponent \(1/2\) . Subsequently, this issue has been extended to other black holes [4]} and gravity theory (Gauss-Bonnet case [5]}, massive gravity case [6]}, Born-Infeld case [7]}, [8]}). A general proof of the existence for these relations between photon orbits and phase transitions were shown in Ref. [9]}.
